Ramanujan’s Master Theorem

S. Ramanujan introduced a technique, known as Ramanujan??s Master Theorem, which provides an explicit expression for the Mellin transform of a function in terms of the analytic continuation of its Taylor coefficients. The history and proof of this result are reviewed, and a variety of applications is presented. Finally, a multi-dimensional extension of Ramanujan??s Master Theorem is discussed.     

Direct and inverse converting between 4-band color space and HSI4: mathematical tool for multispectral image processing of 4 primary colors

Optical Review - In this article, a new mathematical proposal is presented to perform digital multispectral images processing of four primary colors; namely, it shows the method and equations that...     

Multichannel recognition of hydrogen sulphate anion by a Zn(II)–triazole–pyridine complex bearing a ferrocenyl pendant

Receptors ferrocene–triazole–pyridine triads assembled with Zn(II) or Cd(II) metal cations behave as chemosensor molecules for HSO₄ ^?  anions through electrochemical and optical channels: the redox peak of the ferrocene/ferrocenium redox couple is shifted cathodically by 72–53 mV, and a new absorption band appeared in the UV–vis spectrum upon complexation with the HSO₄ ^?  anion. Association constants, detection limits and stoichiometries of the recognition processes have been determined, whereas ¹H NMR experiments and density functional theory calculations are used to suggest the plausible binding mode taking place in the new supramolecular assembly formed.     

Ferrocene-based ureas as multisignaling receptors for anions

The synthesis of structurally new types of ferrocene-based ureas, in which the ferrocene moiety is simultaneously attached to two urea groups, have been prepared directly from 1,1'-bis(isocyanato)ferrocene 1. Homoditopic receptors 2a-e show spectral and electrochemical anion-sensing action: they display a selective downfield shift of the urea protons and a cathodic shift of the ferrocene/ferrocinium redox couple with hydrogen phosphate and fluoride anions. In addition, receptor 2d based on an unprecedent tetraaza[9]ferrocenophane architecture, shows spectral, electrochemical, and selective fluorescent responses to fluoride anion.     

Ultrasonic density measurement cell design and simulation of non-ideal effects

This paper presents a theoretical analysis of a density measurement cell using an unidimensional model composed by acoustic and electroacoustic transmission lines in order to simulate non-ideal effects. The model is implemented using matrix operations, and is used to design the cell considering its geometry, materials used in sensor assembly, range of liquid sample properties and signal analysis techniques. The sensor performance in non-ideal conditions is studied, considering the thicknesses of adhesive and metallization layers, and the effect of residue of liquid sample which can impregnate on the sample chamber surfaces. These layers are taken into account in the model, and their effects are compensated to reduce the error on density measurement. The results show the contribution of residue layer thickness to density error and its behavior when two signal analysis methods are used.     

Regioselective one-pot synthesis of 9-alkyl-6-chloropyrido[3,2-e][1,2,4]triazolo[4,3-a]pyrazines. Reactivity of aliphatic and aromatic hydrazides

[reaction: see text] The one-pot synthesis of new 9-alkyl-6-chloropyrido[3,2-e][1,2,4]triazolo[4,3-a]pyrazines has been achieved. Hydrazides regioselectively reacted as nucleophiles with the 3-chloro substituent of 2,3-dichloropyrido[2,3-b]pyrazine. An intramolecular cyclization afforded the tricycle nonxanthine adenosine receptor antagonists.     

Comparison of UV derivative-spectrophotometry and partial least-squares (PLS-1) calibration for determination of methotrexate and leucovorin in biological fluids

Binary mixtures of methotrexate (MTX) and leucovorin (LV) have been resolved by application of first-derivative spectrophotometry and partial least squares calibration (PLS-1). By measuring the first-derivative signals of MTX and LV at 354 and 300 nm, respectively, simultaneous determination was possible. The mean recoveries for urine samples were 91 and 96% for MTX and LV, respectively. Partial least squares (PLS-1) multivariate calibration has been applied to the determination of these compounds in serum and in urine without pretreatment of the samples. The absorption spectra of serum or urine samples spiked with methotrexate and/or leucovorin, were used to optimize the calibration matrixes by the PLS-1 method. The sensitivity and selectivity of the proposed procedures were calculated. Mean recoveries were 101 and 97% for MTX and LV, respectively, for serum samples, and 101 and 98% for MTX and LV, respectively, for urine samples.